1. Technical Field
This application is related to the field of digital communication, and more particularly, to digital modulation, transmitters, and receivers.
2. Background Technology
Low probability of intercept (LPI) and low probability of detection (LPD) communications employing frequency-hopping code division multiple access (FH-CDMA) and direct-sequence code division multiple access (DS-CDMA) are the most common form of LPI/LPD modulation, with uses in both tactical and commercial applications.
DS-CDMA adds redundancy by spreading the instantaneous bandwidth of the signal, effectively trading data-rate and spectral efficiency for processing gain. There is, however, a limit to the achievable spreading bandwidth, as the information-theoretic capacity starts decreasing towards zero with increasing bandwidth in frequency selective fading.
Multi-tone frequency shift keying (MT-FSK) can approach the information-theoretic capacity in frequency selective fading with increasing bandwidth. Further, by operating over a very wide bandwidth, MT-FSK encoded signals are more difficult to intercept and/or detect. However, detecting these tones in potentially crowded spectral environment requires a receiver capable of operating over a very wide instantaneous bandwidth. Because of practical limitations on the instantaneous bandwidth over which any single receiver can operate, many systems include multiple receivers, negatively affecting cost, size, weight, and power requirements.
Candes, E. and Wakins, M., “An introduction to compressive sampling,” IEEE Signal Processing Magazine, Vol. 8, pp. 21-30 (2008) discloses an electronic compressed sensing receiver that is intended to extend the instantaneous bandwidth by random sampling. However, this approach is believed to be ill-suited for commercial off-the-shelf analog-to-digital converters, whose sample-and-hold circuitry is generally very well matched to the maximum sample rate, such that oversampling will lead to signal attenuation beyond the Nyquist rate.
Compressed sensing receivers and methods are also discussed in J. I. Goodman, et al, “Polyphase Nonlinear Equalization of Time-Interleaved Analog-to-Digital Converters”, IEEE Journal of Selected Topics in Signal Processing, Vol. 3, Issue 3, June 2009; B. A. Miller, J. I. Goodman et al, “A Multi-Sensor Compressed Sensing Receiver: Performance Bounds and Simulated Results” “The Forty Third Asilomar Conference on Signals, Systems and Computes”, November 2009; and J. I. Goodman, K. W. Forsythe, B. A. Miller, “Efficient Reconstruction of Block Sparse Signals”, IEEE Statistical Signal Processing Workshop, June 2011, pp. 629-632.
Various digital modulation formats, as well as transmission and receiving systems, are described in J. I. Goodman, T. G. Macdonald, “Communications Applications”, in “High Performance Embedded Computing Handbook: A Systems Perspective”, M. M. Vai, R. A. Bond, D. R. Martinez, editors, Chapter 30, pp. 425-436, 2008.